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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.sinc.sinc_overview"></a><a class="link" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal and Hyperbolic
      Sinus Cardinal Functions Overview</a>
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<p>
        The <a href="http://mathworld.wolfram.com/SincFunction.html" target="_top">Sinus Cardinal
        family of functions</a> (indexed by the family of indices <code class="literal">a
        &gt; 0</code>) is defined by
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb20.svg"></span>

        </p></blockquote></div>
<p>
        it sees heavy use in signal processing tasks.
      </p>
<p>
        By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic
        Sinus Cardinal</a> family of functions (also indexed by the family of
        indices <code class="literal">a &gt; 0</code>) is defined by
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb22.svg"></span>

        </p></blockquote></div>
<p>
        These two families of functions are composed of entire functions.
      </p>
<p>
        These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a>
        and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>) are needed
        by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our
        implementation</a> of <a href="http://mathworld.wolfram.com/Quaternion.html" target="_top">quaternions</a>
        and <a href="http://mathworld.wolfram.com/Octonion.html" target="_top">octonions</a>.
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple) and
          Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span>
        </p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../graphs/sinc_pi_and_sinhc_pi_on_r.png"></span>
        </p></blockquote></div>
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      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
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      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
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